Rotor-driven spin diffusion in natural-abundance 13C spin systems

Determination of internuclear distances in uniformly labeled molecules by rotational-resonance solid-state NMR

Rotational-resonance magic-angle spinning NMR experiments are frequently used to measure dipolar couplings and to determine internuclear distances. So far most measurements were performed on samples containing isolated spin pairs. Thus, extensive structure elucidation, for example in biomolecules, requires the preparation of a whole set of doubly labeled samples. Here, we describe the analysis of the rotational-resonance polarization-exchange curves obtained from a single, uniformly labeled sample. It is shown experimentally that, at a magnetic field of 14.09 T, the rotational-resonance conditions in uniformly (13)C-labeled threonine are sufficiently narrow to permit the measurement of five distances between the four carbon spins with an accuracy of better than 10%. The polarization-exchange curves are analyzed using a modified two-spin model consisting of the two active spins. The modified model includes an additional offset in the final polarization, which comes from the coupling to the additional, passive, spins. The validity of this approach is experimentally verified for uniformly (13)C-labeled threonine. The broader applicability of such a model is demonstrated by numerical simulations which quantify the errors as a function of the most relevant parameters in the spin system.

Characterization of (1)H-(1)H distances in a uniformly (2)H,(15)N-labeled SH3 domain by MAS solid-state NMR spectroscopy (section sign)

In this communication, we demonstrate the feasibility of obtaining long-range (1)H-(1)H distance information by MAS solid-state NMR for a microcrystalline, uniformly (2)H,(15)N-labeled sample of a SH3 domain of chicken alpha-spectrin. The experiments yield NOESY-type spectra and rely on the favorable dispersion of the (15)N chemical shifts of the protein backbone. Perdeuteration of nonexchangeable sites is employed to simplify proton spin systems and to obtain multiple structural information. Two mixing schemes, (1)H-(1)H double quantum filtered Post-C7 and (1)H spin diffusion, are implemented to obtain quantitative (1)H-(1)H distance information. Post-C7 and spin diffusion cross-peak buildup rates are discussed for initial-rate fitting and in the framework of n = 0 rotational resonance (rotor driven spin diffusion), respectively. Different deuteration schemes were tested to find conditions where short-range (1)H-(1)H interactions are truncated (e.g., between H(N) and H(alpha)), but long-range interactions are retained (e.g., between H(N) and H(N)).

Proton dipolar recoupling in resin-bound peptides under high-resolution magic angle spinning

Rotational resonance and radiofrequency-driven dipolar recoupling (RFDR) experiments have been used to recover the weak proton dipolar interaction present in peptides bound to swollen resins spun at the magic angle. The intensity of the correlation peaks obtained using these sequences is shown to be significantly stronger than the one obtained using the classical NOESY experiment. In addition, it is found that during the relatively long mixing times required to transfer magnetization in such soft materials, the RFDR sequence also achieves magnetization transfer via the scalar J-coupling.

Biomolecular solid state NMR: advances in structural methodology and applications to peptide and protein fibrils

Solid state nuclear magnetic resonance (NMR) methods can provide atomic-level structural constraints on peptides and proteins in forms that are not amenable to characterization by other high-resolution structural techniques, owing to insolubility, high molecular weight, noncrystallinity, or other characteristics. Important examples include peptide and protein fibrils and membrane-bound peptides and proteins. Recent advances in solid state NMR methodology aimed at structural problems in biological systems are reviewed. The power of these methods is illustrated by experimental results on amyloid fibrils and other protein fibrils.

Spin-1/2 and beyond: a perspective in solid state NMR spectroscopy

Novel applications of solid state nuclear magnetic resonance (NMR) to the study of small molecules, synthetic polymers, biological systems, and inorganic materials continue at an accelerated rate. Instrumental to this uninterrupted expansion has been an improved understanding of the chemical physics underlying NMR. Such deeper understanding has led to novel forms of controlling the various components that make up the spin interactions, which have in turn redefined the analytical capabilities of solid state NMR measurements. This review presents a perspective on the basic phenomena and manipulations that have made this progress possible and describes the new opportunities and challenges that are being opened in the realms of spin-1/2 and quadrupole nuclei spectroscopies.

Backbone and side-chain 13C and 15N signal assignments of the alpha-spectrin SH3 domain by magic angle spinning solid-state NMR at 17.6 Tesla

The backbone and side-chain 13C and 15N signals of a solid 62-residue (u-13C,15N)-labelled protein containing the alpha-spectrin SH3 domain were assigned by two-dimensional (2D) magic angle spinning (MAS) 15N-13C and 13C-13C dipolar correlation spectroscopy at 17.6 T. The side-chain signal sets of the individual amino acids were identified by 2D 13C-13C proton-driven spin diffusion and dipolar recoupling experiments. Correlations to the respective backbone nitrogen signals were established by 2D NCACX (CX=any carbon atom) experiments, which contain a proton-nitrogen and a nitrogen-carbon cross-polarisation step followed by a carbon-carbon homonuclear transfer unit. Interresidue correlations leading to sequence-specific assignments were obtained from 2D NCOCX experiments. The assignment is nearly complete for the SH3 domain residues 7-61, while the signals of the N- and C-terminal residues 1-6 and 62, respectively, outside the domain boundaries are not detected in our MAS spectra. The resolution observed in these spectra raises expectations that receptor-bound protein ligands and slightly larger proteins (up to 20 kDa) can be readily assigned in the near future by using three-dimensional versions of the applied or analogous techniques.

Fast MAS total through-bond correlation spectroscopy

Mixing sequences for total through-bond correlation spectroscopy in solids (TOBSY) were developed. The motivation is the design of broadband, effective, and robust sequences adapted for "fast" MAS. Possible sequences with the desired Hamiltonian (the homonuclear isotropic J interaction) were identified using lowest order average Hamiltonian theory. Numerical simulations as a function of the MAS frequency were then employed to further characterize the performance. An experimental TOBSY spectrum of a uniformly (13)C-labeled decapeptide at 20 kHz MAS was obtained using one of the new sequences. The spectrum allows us to assign the (13)C resonances to the respective spin systems.

Double-quantum excitation in the NMR of spinning solids by pulse-assisted rotational resonance

We describe a new technique for double-quantum excitation in magic-angle-spinning NMR of powdered solids. The technique is designed to efficiently excite double-quantum coherence in the vicinity of a rotational resonance condition. The offset from rotational resonance allows the double-quantum filtered signals to be observed with high resolution and sensitivity. The method uses rotational excitation of zero-quantum coherence, assisted by radiofrequency pulse cycles. The zero-quantum coherence is converted into double-quantum coherence by a frequency-selective inversion sequence. Experiments on [(13)C(2), (15)N]-glycine demonstrate a double-quantum filtering efficiency of approximately 41% at a sample rotation frequency of 8.300 kHz, which is 1.600 kHz away from the n = 1 rotational resonance. We achieve 32% double-quantum filtering efficiency at a spinning frequency of 9.250 kHz, which is 2.550 kHz away from rotational resonance.

Coherence transfer signals in the rotational resonance NMR of a spinning single crystal

A recent analysis of rotational resonance lineshapes (M. Helmle et al., J. Magn. Reson. 140, 379-403, 1999) predicted the existence of coherence transfer signals, which are generated by mechanically induced coherence transfer during the detection process. These signals correspond to the generation of observable coherences at spin sites that have no magnetization at the beginning of the observation interval but which acquire coherence while the detection is underway. The coherence transfer signals disappear for powder samples in conventional magic-angle-spinning solid-state NMR experiments. In this Communication, we report the successful detection of coherence transfer signals in rotor-synchronized experiments performed on a single crystal of [1,2-(13)C(2)]glycine. Copyright 2000 Academic Press.

Spinning-frequency-dependent narrowband RF-driven dipolar recoupling

Dipolar recoupling techniques of homonuclear spin pairs are commonly used for distance or orientation measurements in solids. Accurate measurements are interfered with by broadening mechanisms. In this publication narrowband RF-driven dipolar recoupling magnetization exchange experiments are performed as a function of the spinning frequency to reduce the effect of zero-quantum T(2) relaxation. To enhance the exchange of magnetization between the coupled spins, a fixed number of rotor-synchronous pi-pulses are applied at spinning frequencies approaching the rotational resonance (R(2)) conditions. The analysis of the powder averaged dipolar decay curves of the spin magnetizations as a function of the spinning frequency provides a quantitative measure of the dipolar coupling. An effective Hamiltonian for this experiment is derived, taking into account all chemical shift parameters of the spins. The length of the nbRFDR mixing time and the number of rotor cycles per pi-pulse are optimized by numerical simulations for sensitive probing of the dipolar coupling strength. The zero-quantum T(2) relaxation time can easily be taken into account in the data analysis, because the overall exchange time is almost constant in these experiments. Spinning-frequency-dependent nbRFDR experiments near the m = 1 and m = 2 R(2) condition are shown for doubly (13)C-labeled hydroxybutyric acid. Copyright 2000 Academic Press.

Efficient double-quantum excitation in rotational resonance NMR

We present a new technique for double-quantum excitation in magic-angle-spinning solid-state NMR. The method involves (i) preparation of nonequilibrium longitudinal magnetization; (ii) mechanical excitation of zero-quantum coherence by spinning the sample at rotational resonance, and (iii) phase-coherent conversion of the zero-quantum coherence into double-quantum coherence by frequency-selective spin inversion. The double-quantum coherence is converted into observable magnetization by reversing the excitation process, followed by a pi/2 pulse. The method is technically simple, does not require strong RF fields, and is feasible at high spinning frequencies. In [(13)C(2),(15)N]-glycine, with an internuclear (13)C-(13)C distance of 0.153 nm, we achieve a double-quantum filtering efficiency of approximately 56%. In [11, 20-(13)C(2)]-all-E-retinal, with an internuclear (13)C-(13)C distance of 0.296 nm, we obtain approximately 45% double-quantum filtering efficiency.

Multiple-quantum cross polarization in quadrupolar spin systems during magic-angle spinning

We describe the concept of multiple-quantum cross polarization (CP) between an I = 32 and an I = 12 spin during magic-angle spinning. Experimental and theoretical results for (23)Na-(1)H pairs are presented that elucidate the transfer mechanism and the beneficial effect of adiabatic amplitude modulations of the CP field. The multiple-quantum CP approach is shown to be beneficial for improving the sensitivity of CP-MQMAS experiments and for detecting dipolar correlations.

Analysis of dipolar-coupling-mediated coherence transfer in a homonuclear two spin-12 solid-state system

Homonuclear dipolar-mediated coherence transfer (DCT), a through-space transfer of magnetization between like spins, can yield otherwise difficult-to-obtain structural information for macromolecules by measuring the internuclear distances between two sites of interest. The behavior of a spin-12 system under DCT is analyzed in detail by computing the time development of the density matrix using the product operator formalism. The effect of coherence transfer (CT) via the homonuclear isotropic scalar coupling on DCT is examined. Analytical and computational results that yield useful information on the frequencies, first-maxima, and first-zero of CT for a uniaxially oriented or a single-crystal solid-state system are presented. The results predict that the evolution of the spin angular momentum operators under the homonuclear dipolar coupling Hamiltonian leads to "cylindrical mixing" unlike "isotropic mixing" due to the strong scalar coupling Hamiltonian. These results will find relevance in both the design of RF pulse sequences for the structural studies of uniaxially oriented biological solids and the interpretation of solution NMR results from proteins embedded in partially oriented bicelles. Copyright 1999 Academic Press.

Magnetic field gradients in solid state magic angle spinning NMR

Magnetic field gradients have proven useful in NMR for coherence pathway selection, diffusion studies, and imaging. Recently they have been combined with magic angle spinning to permit high-resolution measurements of semi-solids, where magic angle spinning averages any residual dipolar couplings and local variations in the bulk magnetic susceptibility. Here we show the first examples of coherence pathway selection by gradients in dipolar coupled solids. When the gradient evolution competes with dipolar evolution the experiment design must take into account both the strength of the dipolar couplings and the means to refocus it. Examples of both homonuclear and heteronuclear experiments are shown in which gradients have been used to eliminate the need for phase cycling.

Anomalous rotational resonance spectra in magic-angle spinning NMR

Magic-angle spinning NMR spectra of samples containing dilute spin-1/2 pairs display broadenings or splittings when a rotational resonance condition is satisfied, meaning that a small integer multiple of the spinning frequency matches the difference in the two isotropic shift frequencies. We show experimental rotational resonance NMR spectra of a 13C2-labeled retinal which are in qualitative disagreement with existing theory. We propose an explanation of these anomalous rotational spectra involving residual heteronuclear couplings between the 13C nuclei and the neighboring 1H nuclei. These couplings strongly influence the rotational resonance 13C spectrum, despite the presence of a strong radiofrequency decoupling field at the 1H Larmor frequency. We model the residual heteronuclear couplings by differential transverse relaxation of the 13C single-quantum coherences. We present a superoperator theory of the phenomenon and describe a numerical algorithm for rapid Liouville space simulations in periodic systems. Good agreement with experimental results is obtained by using a biexponential transverse relaxation model for each spin site.

High-order spin diffusion mechanisms in (19)F 2-D NMR of oxyfluorides

Negative cross-peaks have been observed in the (19)F 2-D magnetization-exchange MAS NMR spectra of Ba(2)MoO(3)F(4) under fast-spinning conditions. The polarization transfer dynamics are studied as a function of the spinning frequency and the frequency separation of the resonances. The results are consistent with a novel mechanism, in which four spins simultaneously exchange Zeeman magnetization with each other, in an energy-conserving process.

2D exchange NMR spectra under slow MAS: A simplified scheme to obtain pure-phase spectra without unwanted cross peaks

A simplified method for acquiring pure-phase two-dimensional exchange spectra under slow magic-angle spinning (MAS) is introduced. It combines rotor-synchronized 2D exchange spectroscopy with whole-echo acquisition leading to a simplification in data acquisition and data processing compared to the States-type data sampling using "time reversal" (A. Hagemeyer et al., Adv. Magn. Reson. 13, 85 (1989)). As an added benefit, it allows for well-defined mixing times of an arbitrary integer multiple of the MAS rotor period. The proposed method is, however, only applicable to samples where an echo of the free-induction decay can be obtained, i.e., where the inhomogenous linewidth is larger than the homogeneous linewidth. This is, for example, the case in rare-spin spectroscopy of samples with natural isotopic abundance. The usefulness of the new method is demonstrated, using 13C spectroscopy, on two model compounds. Copyright 1999 Academic Press.

19F/29Si distance determination in fluoride-containing octadecasil by Hartmann-Hahn cross-polarization under fast magic-angle spinning

19F/29Si Hartmann-Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated 29Si-19F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si-F internuclear distance, r = 2.62 +/- 0.05 A, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69 +/- 0.04 A recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of approximately 14 kHz is shown to be necessary for an effective suppression of 19F-19F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.

MAS NMR studies of carbon-13 spin exchange in durene

One- (1-D) and two-dimensional (2-D) carbon-13 NMR exchange measurements in powder samples of isotopically normal durene under magic angle spinning (MAS) are reported. The experiments include rotor synchronized 2-D exchange (RS2DE), 1-D magnetization transfer (MT) and time reverse ODESSA (tr-ODESSA). The latter two experiments were performed as a function of several external parameters, including proton decoupling field during mixing time, sample spinning rate and partly, of temperature. The effects of these parameters on the spin exchange induced by spin diffusion and by chemical, or physical exchange, is discussed. Spin exchange between all types of carbons in the durene molecules occurs on the time scale of seconds. From the dependence of the spin exchange rate on the external parameters it is concluded that the process is dominated by spin diffusion. On the basis of these results an upper limit of 10(-16) cm2 s(-1) can be set for the self-diffusion constant in crystalline durene.

Broadband dipolar recoupling in rotating solids: a numerical comparison of some pulse schemes

A numerical comparison of the dipolar recoupling performance of several previously published homonuclear recoupling schemes under magic angle-spinning conditions is presented. Emphasis is put on the recoupled polarization transfer in a two-spin system where the efficiency is studied as a function of resonance offsets in the presence and absence of chemical-shielding anisotropies. In addition, the effect of the rf field strength is investigated. Powder pattern line shapes are shown in the on-resonance case that reveal the distribution of dipolar couplings for each recoupling scheme. These results are compared to data computed with a purposely misset rf field strength to estimate the pulse scheme sensitivity to rf-inhomogeneity and experimental missettings.

Studies of an Isolated 15 N-15 N Spin Pair. Off-Angle Fast-Sample-Spinning NMR and Self-Consistent-Field Calculations for Diazo Systems

An off-magic-angle spinning study of the nonassociated molecular solid, doubly 15 N-labeled 5-methyl-2-diazobenzenesulphonic acid hydrochloride (I ) is reported. The validity of the off-magic-angle spinning approach under fast-spinning conditions is verified by average Hamiltonian theory. Ab initio SCF calculations were performed on the simpler molecule, C6 H5 N2 + , to provide the shielding parameters, the dipolar coupling between the two nitrogen nuclei, and the electric field gradient existing at both the alpha-nitrogen and beta-nitrogen sites. The calculated values are in good agreement with the shielding and effective dipolar coupling data elucidated in the present investigation, and with a previous study of the two singly 15 N-labeled isotopomers in which information concerning the electric field gradient at the alpha and beta sites was deduced.

Distance measurements in nucleic acids using windowless dipolar recoupling solid state NMR

A windowless, homonuclear dipolar recoupling pulse sequence (DRAWS) is described and a theoretical basis for describing its recoupling performance is developed using numerical techniques. It is demonstrated that DRAWS recouples weak dipolar interactions over a broad range of experimental and molecular conditions. We discuss two spectroscopic control experiments, which help to take into account effects due to insufficient proton decoupling, relaxation, and static dipolar couplings to nearby 13C spins at natural abundance. Finally DRAWS is used in combination with selective 13C labeling to measure 13C-13C distances in five doubly labeled DNA dodecamers, [d(CGCGAAT*T*CGCG)]2, which contain the binding site for the restriction enzyme EcoRI. The longest distance reported is 4.8 A. In most cases the distances agree well with those derived from X-ray crystallographic data, although small changes in hydration level can result in relatively large changes in internuclear distances.

Proton spin diffusion for spatial heterogeneity and morphology investigations of polymers

The diffusion of Zeeman spin order in the laboratory frame for a system with microscopic spatial heterogeneity, due to either molecular mobility or chemical heterogeneity, has been analysed by solving the diffusion equation in the limit of two different models. By simulation of proton spin diffusion nuclear magnetic resonance (NMR) spectral areas for poly(ethylene oxide) we have demonstrated, for both models, the sensitivity of these observables to phase domain size and to the dimensionality of the diffusion process. The possibility to obtain information about the morphology is analysed. Results from calculations based on the two models are compared with experimental spin diffusion results from 1H NMR spectra of poly(ethylene oxide). Two methods for filtering the z-magnetization from the different phase domains in a solid are discussed. The efficiency of a magnetization dipolar filter based on magic and polarization echoes is presented.